This invention is directed to the perception and recognition of audio signal inputs and, more particularly, to a signal processing method and apparatus for providing a nonlinear frequency analysis of temporally structured signals in a manner which more closely mimics the operation of the human brain.
The use of an array of nonlinear oscillators to process input audio signal is known in the art from U.S. Pat. No. 7,376,562 granted to Edward W. Large (Large).
It is generally known from Large to process signals using networks of nonlinear oscillators. Nonlinear resonance provides a wide variety of behaviors that are not observed in linear resonance (e.g. neural oscillations). Moreover, as in nature, oscillators can be connected into complex networks. FIG. 1 shows a typical architecture used to process acoustic signals. It consists of a network 100 of layers of one-dimensional arrays of nonlinear oscillators, called gradient-frequency nonlinear oscillator networks (GFNNs). In FIG. 1, GFNNs are arranged into processing layers to simulate auditory processing by two different brain areas (102) at Layer 1 (the input layer) and (104) at Layer 2.
More specifically, as illustrated in FIG. 2, an exemplary nonlinear oscillator system is comprised of a network 402 of nonlinear oscillators 4051, 4052, 4053 . . . 405N. An input stimulus layer 401 can communicate an input signal to the network 402 through a set of the stimulus connections 403. In this regard, the input stimulus layer 401 can include one or more input channels 4061, 4062, 4063 . . . 406C. The input channels can include a single channel of multi-frequency input, two or more channels of multi-frequency input.
Assuming C input channels as shown in FIG. 2, then the stimulus on channel 406C at time t is denoted xC (t), and the matrix of stimulus connections 403 may be analyzed as strength of a connection from an input channel 406C to an oscillator 405N, for a specific resonance, as known from Large. Notably, the connection matrix can be selected so that the strength of one or more of these stimulus connections is equal to zero.
As known from Large, signal processing by networks of nonlinear oscillators can be performed to broadly mimic the brain's response. This is similar to signal processing by a bank of linear filters, but with the important difference that the processing units are nonlinear, rather than linear oscillators. In this section, this approach is explained by comparing it with linear time-frequency analysis.
A common signal processing operation is frequency decomposition of a complex input signal, for example by a Fourier transform. Often this operation is accomplished via a bank of linear bandpass filters processing an input signal, x(t). For example, a widely used model of the cochlea is a gammatone filter bank (Patterson, et al., 1992). For comparison with our model a generalization can be written as a differential equationż=z(α+iω)+x(t)  (1)
where the overdot denotes differentiation with respect to time (i.e., dz/dt), z is a complex-valued state variable, ω, is radian frequency (ω=2πf, f in Hz), α<0 is a linear damping parameter. The term, x(t), denotes linear forcing by a time-varying external signal. Because z is a complex number at every time, t, it can be rewritten in polar coordinates revealing system behavior in terms of amplitude, r, and phase, φ. Resonance in a linear system means that the system oscillates at the frequency of stimulation, with amplitude and phase determined by system parameters. As stimulus frequency, ω0, approaches the oscillator frequency, ω, oscillator amplitude, r, increases, providing band-pass filtering behavior.
Recently, nonlinear models of the cochlea have been proposed to simulate the nonlinear responses of outer hair cells. It is important to note that outer hair cells are thought to be responsible for the cochlea's extreme sensitivity to soft sounds, excellent frequency selectivity and amplitude compression (e.g., Egulluz, Ospeck, Choe, Hudspeth, & Magnasco, 2000). Models of nonlinear resonance that explain these properties have been based on the Hopf normal form for nonlinear oscillation, and are generic. Normal form (truncated) models have the formż=z(α+iω+β|z|2)+x(t)+h.o.t.  (2)
Note the surface similarities between this form and the linear oscillator of Equation 1. Again ω is radian frequency, and α is still a linear damping parameter. However in this nonlinear formulation, a becomes a bifurcation parameter which can assume both positive and negative values, as well as α=0. The value α=0 is termed a bifurcation point. β<0 is a nonlinear damping parameter, which prevents amplitude from blowing up when α>0. Again, x(t) denotes linear forcing by an external signal. The term h.o.t. denotes higher-order terms of the nonlinear expansion that are truncated (i.e., ignored) in normal form models. Like linear oscillators, nonlinear oscillators come to resonate with the frequency of an auditory stimulus; consequently, they offer a sort of filtering behavior in that they respond maximally to stimuli near their own frequency. However, there are important differences in that nonlinear models address behaviors that linear ones do not, such as extreme sensitivity to weak signals, amplitude compression and high frequency selectivity. The compressive gammachirp filterbank exhibits similar nonlinear behaviors, to Equation 2, but is formulated within a signal processing framework (Irino & Patterson, 2006).
Large taught expanding the higher order terms of Equation 2 to enable coupling among oscillators of different frequencies. This enables efficient computation of gradient frequency networks of nonlinear oscillators, representing an improvement to the technology. As known from applicant's copending application Ser. No. 13/016,713, the canonical model (Equation 3) is related to the normal form (Equation 2; see e.g., Hoppensteadt & lzhikevich, 1997), but it has properties beyond those of Hopf normal form models because the underlying, more realistic oscillator model is fully expanded, rather than truncated. The complete expansion of higher-order terms produces a model of the form
                                          z            .                    =                                    z              (                              α                +                                  i                  ⁢                                                                          ⁢                  ω                                +                                                      (                                                                  β                        1                                            +                                              i                        ⁢                                                                                                  ⁢                                                  δ                          1                                                                                      )                                    ⁢                                                                                  z                                                              2                                                  +                                  ε                  ⁢                                                                                    (                                                                              β                            2                                                    +                                                      i                            ⁢                                                                                                                  ⁢                                                          δ                              2                                                                                                      )                                            ⁢                                                                                                  z                                                                          4                                                                                    1                      -                                              ε                        ⁢                                                                                                          z                                                                                2                                                                                                                                )                        +                          c              ⁢                                                          ⁢                              𝒫                ⁡                                  (                                      ε                    ,                                          x                      ⁡                                              (                        t                        )                                                                              )                                                                    ,                  𝒜          ⁡                      (                          ε              ,                              z                _                                      )                                              (        3        )            
There are again surface similarities with the previous models. The parameters, ω, α and β1 correspond to the parameters of the truncated model. β2 is an additional amplitude compression parameter, and c represents strength of coupling to the external stimulus. Two frequency detuning parameters δ1 and δ2 are new in this formulation, and make oscillator frequency dependent upon amplitude. The parameter E controls the amount of nonlinearity in the system. Most importantly, coupling to a stimulus is nonlinear and has a passive part, P(ε,x(t)) and an active part, A(ε, z), producing nonlinear resonances.
Equation 3 above is generally stated in terms of x(t) wherein x(t) is the input audio source signal. However, in the human brain, neural oscillators experience sound not only from the exterior environment, but signals input from other oscillators either across the array layer or between layers of array, which would include feedback as shown in FIG. 1a between oscillator layers, inputs from oscillator layers both above and below the subject oscillator, and the like. Equation 3 accounts for these different inputs, but for ease of explanation, utilizes a generic x(t).
The Large method and system for the behavior of a network of nonlinear oscillator better mimics the complexity of the ear response to complex audio signals than the prior art linear models. However, it suffers from the disadvantage that it does not include a method for tracking changes in frequency of an input signal. Moreover, digital implementations of this system require significant computation which may limit applications that require real-time operation.